Strings as sigma models and in the tensionless limit

Abstract

This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models. The tensionless limit is used to find a IIB supergravity background generated by a tensionless string. Quantization of the tensionless string in a pp-wave background is performed and the tensionless limit is found to commute with quantization. Further, the sigma model with N=(2,2) extended world-sheet supersymmetry is considered and the requirement on the target space to have a bi-Hermitean geometry is reviewed. It is shown that the equivalence between bi-Hermitean geometry and generalized Kahler follows, in this context, from the equivalence between the Lagrangian- and Hamiltonian formulation of the model. Moreover, the explicit T-duality transformation in the Hamiltonian formulation of the sigma model is constructed and shown to be a symplectomorphism. Under certain assumptions, the amount of extended supersymmetry present in the sigma model is shown to be preserved under T-duality. Further, by requiring N=(2,2) extended supersymmetry in a first order formulation of the sigma model an intriguing geometrical structure arises and in a special case generalized complex geometry is found to be contained in the new framework.

PhD Thesis, viii+127 pages

References in corpus (26)

• Dirichlet-Branes and Ramond-Ramond Charges
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• Rolling Tachyon
• Tachyon Matter
• Penrose limits and maximal supersymmetry
• Exactly solvable model of superstring in Ramond-Ramond plane wave background
• Duality, Quotients, and Currents
• Some Comments On String Dynamics
• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• Classical and Quantized Tensionless Strings
• The Plane-Wave/Super Yang-Mills Duality
• Current Algebras and Differential Geometry
• Lectures on the Plane-Wave String/Gauge Theory Duality
• Tensionless Strings, WZW Models at Critical Level and Massless Higher Spin Fields
• New aspects of the ddc-lemma
• D-strings and F-strings from string loops
• Generalized N=(2,2) Supersymmetric Non-Linear Sigma Models
• Hamiltonian perspective on generalized complex structure
• Off-Shell Formulation of N=2 Non-Linear Sigma-Models
• Lectures on Generalized Complex Geometry and Supersymmetry
• Generalized complex geometry and the Poisson Sigma Model
• Generalized Hyperkaehler Geometry and Supersymmetry
• First-order supersymmetric sigma models and target space geometry
• Supersymmetric WZ-Poisson sigma model and twisted generalized complex geometry
• T-duality and Generalized Complex Geometry
• A note on N=(2,2) superfields in two dimensions